A276532 a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5)) / a(n-7), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1.

1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 11, 41, 371, 7507, 429563, 419408854, 9811194604889, 45615501062085527113, 323645006689468299915979814409, 217332607887523478570092794860281557159140687, 8092345737591989154121803868154457767563221634145658745306515944569

Offset

0,8

Comments

This sequence is one generalization of Dana Scott's sequence (A048736).

a(n) is integer for all n.

The recursion exhibits the Laurent phenomenon. See A278706 for the exponents of the denominator of the Laurent polynomial. - Michael Somos, Nov 26 2016

Links

Seiichi Manyama, Table of n, a(n) for n = 0..26

Formula

a(n) * a(n-7) = a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5).

a(6-n) = a(n) for all n in Z.

Prog

(Ruby)
def A(k, n)
  a = Array.new(k, 1)
  ary = [1]
  while ary.size < n + 1
    i = a[-1] * a[1] + a[2..-2].inject(:*)
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276532(n)
  A(7, n)
end

Crossrefs

Cf. A048736, A006721, A276531, A278706.

Sequence in context: A222007 A188142 A276531 * A003686 A086506 A109462

Adjacent sequences: A276529 A276530 A276531 * A276533 A276534 A276535

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2016

Status

approved